Question 74
$\triangle P N R$ has side lengths $P N = 20$, $N R = 18$, and $P R = 19$. Consider a point $A$ on $P N$. $\triangle N R A$ is rotated about $R$ to $\triangle N' R A'$, so that $R$, $N'$, and $P$ lie on the same line and $A A'$ is perpendicular to $P R$. Find $\frac{P A}{A N}$.